Draw EX//BA and FX//BC ( see picture)1, 2. We have ( AEX)=(BAE)= a and (AFX)=(FAD)= b ---- (properties of // lines)EX and EY are angle bisectors of (AED) and (AFB)So (AED)=2(BAE)= 2a and (AFB)=2(DAF)=2b

3. From the picture we have (EAF)= 90-a-b -------(1)(FNY)=b+(YXF)(EXY)=a+(YXE)(FNY)+(EXY)= a+b+(EXF)=90+a+b= ( GNH) ---- (2)Add (1)+(2) side by side : (EAF)+(GNH)=1804. and A,G,N,H are concyclic